What is a common misconception about fractions among students?

A common misconception among students regarding fractions is that fractions less than 1 represent improper fractions. However, the definition of improper fractions is actually those that are greater than or equal to 1, where the numerator is greater than or equal to the denominator.

When students encounter fractions like ( \frac{1}{2} ) or ( \frac{3}{4} ), they mistakenly think these are improper fractions simply because they are less than 1. This misunderstanding can hinder their ability to compare fractions and perform operations involving them. Recognizing that proper fractions, which are less than 1, and improper fractions, which are equal to or greater than 1, are distinct categories is essential for developing a strong foundation in working with fractions.